Unique maximal Betti diagrams for Artinian Gorenstein k -algebras with the weak Lefschetz property

We give an alternate proof for a theorem of Migliore and Nagel. In particular, we show that if H is an SI-sequence, then the collection of Betti diagrams for all Artinian Gorenstein k-algebras with the weak Lefschetz property and Hilbert function H has a unique largest element.